Homework 5.5 Solving Quadratics Part 3
Answer the following questions about solving quadratics.
1. What are the solving methods to solve for quadratic equations? Fill in the methods in the diagram below.
2 Terms (Binomials)
1. ________________________
2. ________________________
3. ________________________
3 Terms (Trinomials)
1. ________________________
2. ________________________
3. ________________________
4. ________________________
2. In order to solve for x by using the complete the square method, you must ________________________.
3. In order to solve for x by using the quadratic formula method, you must ___________________________.
4. How do we determine how many solutions a quadratic equation has? ______________________________.
Determine the number of roots each quadratic will have.
5. −5𝑎 2 + 10𝑎 − 6 6. −3𝑛 2 + 11𝑛 − 10 = 0 7. 8𝑥 2 + 6𝑥 − 12 = 0
8. −𝑣 2 + 4𝑣 + 5 = 9
+ 14𝑎 − 51 = 0
9. 5𝑥
Solve by completing the square method.
2 − 10𝑥 + 18 = 13
12. 𝑥 2
10. −4𝑥
− 12𝑥 + 11 = 0
2 + 𝑥 − 15 = −13
11. 𝑎 2

11. 𝑎 2
Homework 5.5 Solving Quadratics Part 3 Solutions
Answer the following questions about solving quadratics.
1. What are the solving methods to solve for quadratic equations? Fill in the methods in the diagram below.
2 Terms (Binomials)
1. GCF Factoring
2. Difference of Squares
3. Taking Square Root
3 Terms (Trinomials)
1. GCF Factoring
2. Factoring Trinomials
3. Completing the Square
4. Quadratic Formula
2. In order to solve for x by using the complete the square method, you must isolate the constant term.
3. In order to solve for x by using the quadratic formula method, you must set the equation equal to 0.
4. How do we determine how many solutions a quadratic equation has? Use the discriminant; 𝑏 2
Determine the number of roots each quadratic will have.
5. −5𝑎 2 + 10𝑎 − 6
No real solutions, but 2 imaginary solutions
6. −3𝑛 2 + 11𝑛 − 10 = 0
2 real solutions
7. 8𝑥 2 + 6𝑥 − 12 = 0
2 real solutons
10. −4𝑥 2 + 𝑥 − 15 = −13 8. −𝑣 2 + 4𝑣 + 5 = 9
1 real solution
9. 5𝑥
Solve by completing the square method.
2 − 10𝑥 + 18 = 13
1 real solution No real solutions, but 2 imaginary solutions
− 4𝑎𝑐 .
+ 14𝑎 − 51 = 0 𝑎 = 3, 𝑎 = −17
12. 𝑥 2 − 12𝑥 + 11 = 0 𝑥 = 11 𝑥 = 1

Homework 5.5 Solving Quadratics Part 3 (Page 2)
13. 𝑥 2 + 14𝑥 = 15 14. 𝑘 2
17. 9𝑥 2
15. 𝑘 2 − 4𝑘 + 1 = −5
Solve by using the quadratic formula method.
+ 9𝑥 + 10 = 0
16.
18.
20. 𝑏 2
6𝑥
7𝑥
2
2
+ 23 = 12𝑘
+ 2𝑏 = −20
+ 4𝑥 − 20 = 0
− 4𝑥 + 20 = 8 19. 11𝑟 2 − 8𝑟 + 14 = 4
21. 3𝑛 2 = −𝑛 − 10 22. 11𝑏 2 − 16 = −8𝑏

Homework 5.5 Solving Quadratics Part 3 (Page 2)
13. 𝑥 2 + 14𝑥 = 15 𝑥 = 1 𝑥 = −15
14. 𝑘 2
15. 𝑘 2 − 4𝑘 + 1 = −5 𝑘 = 2 + 𝑖√2 𝑘 = 2 − 𝑖√2
16. 𝑏 2
+ 23 = 12𝑘 𝑘 = 6 + √13 𝑘 = 6 − √13
+ 2𝑏 = −20 𝑏 = −1 + 𝑖√19 𝑏 = −1 − 𝑖√19
Solve by using the quadratic formula method.
+ 9𝑥 + 10 = 0 17. 9𝑥 2 𝑥 = − 𝑥 = −
3
6
3
6
+
+ 𝑖√31
6 𝑖√31
6
,
19. 11𝑟 2 − 8𝑟 + 14 = 4 𝑟 = 𝑟 =
4
11
4
11
−
+ 𝑖√94
11 𝑖√94
11
,
21. 3𝑛 2 = −𝑛 − 10 𝑛 = −
= −
1
6
1
6
+
− 𝑖√119
6 𝑖√119
6
18.
20.
22.
6𝑥
7𝑥
2
2
11𝑏 2
+ 4𝑥 − 20 = 0 𝑥 = − 𝑥 = −
− 4𝑥 + 20 = 8 𝑥 = 𝑥 =
− 16 = −8𝑏 𝑏 = − 𝑏 = −
2
7
2
7
1
3
1
3
−
+
4
11
4
11
+
−
4𝑖√5
4𝑖√5
−
+
√31
√31
7
7
3
3
,
8√3
11
8√3
11
Solutions